LsmGANs: Image-Domain Least-Squares Migration Using a New Framework of Generative Adversarial Networks

Compared with the traditional adjoint migration, the least-squares migration (LSM) can effectively mitigate the unbalanced illumination and limited resolution associated with finite acquisition apertures, complex overburden structures, and band-limited records. Data-domain LSM needs many times of Born modeling and adjoint migration to converge to a good solution, which is still challenging for large-scale 3-D models under the current computational capacity. To reduce computational cost and produce high-quality images, we directly approximate the Hessian inverse in the image-domain LSM using a new framework of generative adversarial networks (GANs). The migrated images, source illumination, and migration velocity model are used as input data for the GANs, and the ground-truth reflectivity is utilized as the label data to train the network. Directly applying a conventional GAN framework to implement the image-domain LSM leads to dislocated reflection events and incorrect images. To overcome this issue, we develop a new GAN framework that is more suitable for the Hessian approximation of image-domain LSM, which is named as LsmGANs. In the new framework, we use max-pooling instead of convolution to downsample the feature maps to capture horizontal and vertical variations of reflectors. This enables us to map reflection events to the correct location in downsampling. To address the lateral discontinuity of events in the predicted image from conventional GANs, we further apply multiple transform layers to strengthen feature transformation to guide Hessian approximation. Finally, we add the skip connection in the transform layer to enhance the information exchange of the feature channels and avoid the gradient vanishing problem to improve image resolution. Assembling predicted patches to construct a whole reflectivity image is a key step in the neural network-based LSM. We investigate four strategies using different overlapping ratios and window functions to assemble the LSM patches and observe that less overlapping produces more patch-edge artifacts and the partition of unit with a Gaussian window has the best performance. Numerical experiments for synthetic and field data show that the proposed LsmGAN method can produce high-quality images with balanced amplitudes, reduced artifacts, and improved resolution.